Question 18

Explanation

We will find the height of the helicopter from the helipad ($DC$) using trigonometric ratios in right-angled triangles.

Observe the solution sketch:

Observe the geometry:

• $AD = 16$ m (building height).
• $AB$ is the distance from the building to the tip of the shadow.
• The angle of elevation to the top of the building is $30^\circ$ and to the helicopter is $45^\circ$.

First, we calculate the distance $AB$ using $\tan(30^\circ)$ in triangle $ABD$.

Next, use this distance $AB$ to find the total height of the helicopter from the ground ($AC$) using $\tan(45^\circ)$ in triangle $ABC$.

The height of the helicopter from the helipad is the difference between the total height and the building height.

Thus, the height of the helicopter from the helipad is $16(\sqrt{3} - 1)$ meters.